Thus far our discussion has focused on the information carried by the expression level of just one gene, but we know that positional information is carried by the combined expression levels of all four gap genes [1]}, [2]}. Rather than considering, as above, the mapping \(g_{\rm Hb} \rightarrow C\) , we can consider mappings from combinations of expression levels into compressed variables. We start with Hb and Kr, so we consider \(\lbrace g_{\rm Hb} ,g_{\rm Kr}\rbrace  \rightarrow C\) . The analog of Eq (REF ) is the optimization problem
\(\max _{P(C|\lbrace g_{\rm Hb} ,g_{\rm Kr}\rbrace )} \left[ I(C;x) - T I(C;\lbrace g_{\rm Hb} ,g_{\rm Kr}\rbrace )\right].\) 
